A&A 627, L8 (2019) Astronomy https://doi.org/10.1051/0004-6361/201935835 & c ESO 2019 Astrophysics LETTER TO THE EDITOR Masses of the Hyades white dwarfs A gravitational redshift measurement? L. Pasquini1, A. F. Pala1, H.-G. Ludwig2, I. C. Leao˜ 3, J. R. de Medeiros3, and A. Weiss4 1 ESO, Karl Schwarzschild Strasse 2, 85748 Garching, Germany e-mail: [email protected] 2 Zentrum für Astronomie der Universität Heidelberg, Landessternwarte, Königstuhl 12, 69117 Heidelberg, Germany 3 Departamento de Física, Universidade Federal do Rio Grande do Norte, 59078-970 Natal, RN, Brazil 4 Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany Received 3 May 2019 / Accepted 25 June 2019 ABSTRACT Context. It is possible to accurately measure the masses of the white dwarfs (WDs) in the Hyades cluster using gravitational redshift, because the radial velocity of the stars can be obtained independently of spectroscopy from astrometry and the cluster has a low velocity dispersion. Aims. We aim to obtain an accurate measurement of the Hyades WD masses by determining the mass-to-radius ratio (M/R) from the observed gravitational redshift, and to compare them with masses derived from other methods. Methods. We analyse archive high-resolution UVES-VLT spectra of six WDs belonging to the Hyades to measure their Doppler shift, from which M/R is determined after subtracting the astrometric radial velocity. We estimate the radii using Gaia photometry as well as literature data. Results. The M/R error associated to the gravitational redshift measurement is about 5%. The radii estimates, evaluated with different methods, are in very good agreement, though they can differ by up to 4% depending on the quality of the data. The masses based on gravitational redshift are systematically smaller than those derived from other methods, by a minimum of ∼0.02 up to 0.05 solar masses. While this difference is within our measurement uncertainty, the fact that it is systematic indicates a likely real discrepancy between the different methods. Conclusions. We show that the M/R derived from gravitational redshift measurements is a powerful tool to determine the masses of the Hyades WDs and could reveal interesting properties of their atmospheres. The technique can be improved by using dedicated spectrographs, and can be extended to other clusters, making it unique in its ability to accurately and empirically determine the masses of WDs in open clusters. At the same time we prove that gravitational redshift in WDs agrees with the predictions of stellar evolution models to within a few percent. Key words. white dwarfs – stars: fundamental parameters – open clusters and associations: individual: Hyades 1. Introduction the masses of the Hyades WDs with good accuracy because (i) Gaia provides very accurate distances (to better than 0.5%) for The importance of the accurate determination of stellar mass these stars, and (ii) the Hyades cluster radial velocity is known cannot be overemphasized. Especially for white dwarfs (WDs), with an uncertainty of about 100 ms−1 (Leão et al. 2019). These the mass-to-radius relationship is interesting because it is accu- latter authors have also shown that spectroscopic and astro- rately predicted by stellar physics and evolution, and unlike in metric radial velocities agree to better than ∼30 ms−1 once the other stages of stellar evolution, more massive stars are pre- additional causes of line shifts are properly taken into account: dicted to have smaller radii. The ratio between the initial stel- gravitational redshift, atmospheric convective motions, and clus- lar mass and the mass of WDs for instance is essential to model ter rotation. After applying these corrections, the cluster veloc- stellar populations, and more generally to verify predictions of ity dispersion is small: less than 340 ms−1 (Leão et al. 2019). stellar-evolution models such as cooling times, ages, and masses Therefore, in principle, by measuring the spectral Doppler shift of WDs. A direct comparison between models and observations of the WDs in the Hyades, their gravitational redshift (GR) is therefore fundamental. For example, Salaris & Bedin(2018) can be derived with an error of ∼300 ms−1. In most stars use evolutionary models to estimate the masses of the Hyades the GR is of a few hundred metres per second, comparable WDs with a precision of about 2%. The radii and masses of WDs to the convective blueshifts in stellar atmospheres (see e.g. can be obtained by observing these targets in eclipsing bina- Allende Prieto et al. 2002; Leão et al. 2019), but in WDs the GR ries, to better than 1% accuracy (see e.g. Parsons et al. 2017). signal is very pronounced (tens of km s−1), and, if hotter than We think that it is now possible to observationally determine ∼14 000 K, no other mechanism capable of shifting the lines of these stars is expected to be present (Allende Prieto et al. 2002; ? Based on UVES data from the ESO VLT archive. Tremblay et al. 2013). This implies that the difference between Article published by EDP Sciences L8, page 1 of4 A&A 627, L8 (2019) Table 1. Gravitational redshift measurement. Star Doppler shift ∆v Zucker Ave RV(astro) Rotation GR Reid GR M/R HZ4 82.64 0.7 79.4 81.0 36.29 −0.27 44.4 41.6 69.76 HZ7 75.07 1.0 73.3 74.2 40.39 0.06 33.9 33.5 53.26 LAWD19 74.52 0.2 75.4 75.0 39.55 0.01 35.5 35.4 55.77 LAWD18 73.87 0.8 75.0 74.4 39.15 −0.03 35.2 35.7 55.30 EGGR29 90.16 1.0 93.1 91.6 37.54 −0.15 53.9 52.3 84.68 HG7-85 87.81 2.0 86.3 87.0 37.07 −0.20 49.7 78.08 Notes. Column 1: star id; Col. 2: measured Doppler shift from UVES spectra, averaged between two observations; Col. 3: half difference between the two UVES observations; Col. 4: Doppler shift as measured by Zuckerman et al.(2013) from Keck spectra; Col. 5: UVES and Zuckerman et al. (2013) average Doppler shifts; Col. 6: astrometric radial velocities; Col. 7: correction for cluster rotation; Col. 8: GR (from Cols. 5, 6 and 7); Col. 9: GR from Reid(1996) Keck spectra; Col. 10: M /R from our GR estimate. All columns are expressed in km s−1. the spectroscopic Doppler shifts and the astrometric radial veloc- as measured from the Hα core and averaging the two observa- ity can be attributed entirely to GR, making the measurement tions. The associated error is simply half the difference between potentially very accurate. the two UVES spectra. When adding the other sources of error, White dwarf binaries are also suitable candidates for this we consider that an overall uncertainty of 2 km s−1 is realistic. technique, provided the binary system is very well characterised, We assumed for Hα a wavelength of 6562.801 Å. and GR observations have been used with success for Sirius B to The Doppler shifts were subsequently corrected for the astro- show the equivalence between the GR mass and dynamical mass metric radial velocity of each star and for the cluster rotation, of this star (Joyce et al. 2018). though the latter is less than 300 ms−1 for the sample stars The eight well-established DA WDs (white dwarfs with (Leão et al. 2019), providing the GR for each star. All the val- hydrogen atmospheres) belonging to the Hyades cluster ues obtained are given in Table1. (Salaris & Bedin 2018) are therefore ideal candidates for GR In the same table we also provide the Doppler velocities measurement. measured by Zuckerman et al.(2013) and the GR measured by Reid(1996) with HIRES at Keck. These independent mea- surements agree well with ours, confirming that the assumed 2. Doppler shift and GR measurements 2 km s−1 uncertainty is very reasonable. It is worth noting that The spectral lines of WDs are very broad, and in principle this Zuckerman et al.(2013) used the blue setup of HIRES, which makes the measurement of their Doppler shift relatively diffi- does not provide access to Hα, and higher lines in the Balmer cult. However, the main Balmer lines (notably Hα and some- series were measured. These latter lines do not show narrow times Hβ) show non- local thermodynamic equilibrium (LTE) cores, explaining why their velocities have a comparable uncer- narrow cores, allowing precise measurements of their Doppler tainty to the UVES ones, in spite of the fact that the Keck shifts. This feature has been used in the past to measure GR or to spectra are at a higher resolution and have higher S/N ratios. search for binary progenitors of supernovae (see e.g. Reid 1996; Since other lines as well as another spectrograph were used, the Napiwotzki et al. 2001; Zuckerman et al. 2013). Zuckerman et al.(2013) measurements are complementary and Out of the eight classical DA WDs in the Hyades, six have independent from ours. The maximum difference between the −1 been observed with UVES at the VLT in the early 2000s by Zuckerman et al.(2013) Doppler shift and ours is of 3 km s , in the Supernova-Ia Progenitor Survey (SPY) large programme agreement with our estimated uncertainty. (Napiwotzki et al. 2001) and they are listed in Table1. Each star We finally compute M/R (in solar unit) by averaging the has been observed at two different epochs. The signal to noise UVES and Zuckerman et al.(2013) shifts (also reported in −1 ratio (S/N) for each observation is about 25 in the continuum Table1) and using the formula: GR = 0.6365(M/R) (in km s ).